The gcd of two numbers is 17 and their lcm is 204. one of the numbers is 68. find the other number.

1 answer:

6 0

$x\cdot y=GCD(x,\ y)\cdot LCM(x,\ y)\\\\\text{We have}\\\\x=68,\ GCD=17,\ LCM=204.\\\\\text{Substitute:}\\\\68y=(17)(204)\\\\68y=3,468\qquad\text{divide both sides by 68}\\\\\boxed{y=51}\\\\Answer:\ \boxed{\text{The other number is 51.}}$

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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$\bar X=1.1$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=4.9 represent the sample standard deviation

n=51 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

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Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,50)".And we see that $t_{\alpha/2}=2.02$